Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
In each case we have S (t) → 0 (t → 0) i.e., all of them are Big-Bang
cosmologies. As in the matter dominated scenario, for small t the ¯C term is
dominating, such that, independently of k,
S (t) 4 ¯C 1/4
The behavior for large t is easily obtained:
k=0 : S (t) = 4 ¯C 1/4 (ct) 1/2
k=-1
k=1
:
:
S (t) ct
cyclic, cycle time ctc = 2 √ ¯C
For k = 1 cyclicity is t → t − t0n ; t0n = n · 2 √ ¯C
c .
(ct) 1/2 ; t → 0
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 459